Abstract
Bubbles and spikes in cryptocurrency prices increase considerably the risk on investments in these assets. In the traditional time series literature bubbles are viewed as nonstationary and non-estimable components of a process. In this paper, we adopt a different approach and consider the bubbles as inherent features of a strictly stationary causal-noncausal (mixed) Vector Autoregressive (VAR) process. This approach allows us to model and estimate the common bubbles and spikes in cryptocurrency prices. It also provides us linear combinations of cryptocurrencies that eliminate common bubbles analogously to the cointegrating vectors eliminating common trends in unit root processes. They are used to build cryptocurrency portfolios immune to the risk of common bubbles that ensure stable investment strategies. The mixed VAR model is estimated from the US Dollar prices of Bitcoin, Ethereum, Ripple, and Stellar over the period 2017–2019. We document the common bubbles and illustrate the behaviour of bubble-free portfolios.
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